Uncertainty Visualization in Multiobjective Robust Design Optimization
Sirisha Rangavajhala, Anoop A. Mullur, Achille Messac · 2006
Visualization of the solution of multiobjective problems can be challenging because of high problem dimensionality. In multiobjective robust design optimization problems, additional objective functions, e.g., those related to objective robustness and constraint satisfaction, are typically introduced into the problem. These additional objectives add to the existing high dimensionality of the original problem, making visualization more challenging than deterministic problems. An effective visualization of the relevant information in such problems can significantly aid decision making under uncertainty. We observe that each Pareto optimal solution in multiobjective RDO problems has three uncertainty attributes that can aid the designer in decision making: (1) mean objective performance, (2) variation in performance, and (3) constraint satisfaction. In this paper, we propose a visualization scheme that presents uncertainty information in terms of the above three attributes graphically. The multiobjective problem under uncertainty is first solved to obtain a set of Pareto solutions. Using designer requirements in the above three attributes, a filtering scheme is used to extract relevant data, which is then plotted in the mean objective space. Based on this filtering, desirable regions of the mean objective space from an uncertainty perspective are identified. The proposed visualization scheme is illustrated with the help of a weld assembly design example.